Variants to the cutting plane approach for convex nondifferentiable optimization

We discuss the basic ideas for solving convex nondifferentiable minimization problems through piecewise linear approximations to the objective function. We revise the traditional cutting plane approach by introducing some variants based on suitable translations of the supporting hyperplanes to the epigraph of the function. We describe also somme possible choices for defining a quadratic penalty term on the possible displacement to be added to the model. Finally we report on some numerical experiments on standard test problems.